There are reasons why you might want to do a very large number of repeated invocations of a hash function. This is called Key stretching (see "(A)" below)
However, "very large" is a lot more than 3 ;). Maybe 1,000s or much, much more.
eg maybe see how many invocations you can do in 0.1 sec or 1 sec on the target system, and use that number of hash invocations.
Adjust bcrypt cost to prevent future password hash attacks proposes a method which will keep password hashes strong, even as CPU speeds increase.

Also, you should ideally use a large salt that is different for each user. (see "(B)" below)

A related application is password verification. Storing all user passwords as cleartext can result in a massive security breach if the password file is compromised. One way to reduce this danger is to only store the hash digest of each password. To authenticate a user, the password presented by the user is hashed and compared with the stored hash. (Note that this approach prevents the original passwords from being retrieved if forgotten or lost, and they have to be replaced with new ones.) The password is often concatenated with a random, non-secret salt value before the hash function is applied. The salt is stored with the password hash. (B)Because users have different salts, it is not feasible to store tables of precomputed hash values for common passwords. (A) Key stretching functions, such as PBKDF2, Bcrypt or Scrypt, typically use repeated invocations of a cryptographic hash to increase the time required to perform brute force attacks on stored password digests.

Sorry, but this is just plain stupid. The innermost md5 reduces (or expands) all input to 128 bit. md5_hex around this very likely reduces its input to less than 128 bits (I would be really surprised if all 2^128 possible 128 bit arguments for the MD5 function would result in 2^128 different results). Representing the result in hex adds adds 128 constant bits, so at least half of the input for md5_base64 is constant. Ideally, this would reduce the output of md5_base64 to 2^64 possible values, but due to the previous hash functions, it is likely that the there are far less different values, so the probability for collisions rises. Or shorter: different passwords can result in the same hash value.

zork42++ told you how to properly handle passwords, mainly salting and using strong hash functions. MD5 was strong decades ago, now it should be considered weak.

zork42 also told you about key stretching. Implemented properly, it improves the encryption quality. Read the Wikipeda article. Or just look at the code examples in that article: The key stretching does not add constant bits, but varying bits from the input.

Alexander

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Today I will gladly share my knowledge and experience, for there are no sweeter words than "I told you so". ;-)